Chiral vector is in the direction along which the graphite sheet is rolled up to form a nanotube and it defines a carbon nanotube through three basic patterns: zig-zag, with chiral angle [theta] = 0[degrees] armchair with chiral angle [theta] = 30[degrees] and basic chiral nanotube with chiral angle in the range 0[degrees] < [theta] < 30[degrees] In Eq.

Thus the vectors (0,n) and (m,0) denote zig-zag nanotubes, the vectors (m,m) or (n,n) denote armchair nanotubes and all other vectors correspond to chiral nanotubes.

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